The first-order coherence function is defined as [1]}, [2]}
\( g^{(1)}_N({\bf r}) =\frac{\langle \hat{\psi }^\dag ({\bf 0})\hat{\psi }({\bf r})\rangle _N}{\sqrt{\langle \hat{\psi }^\dag ({\bf 0})\hat{\psi }({\bf 0})\rangle }_N \sqrt{\langle \hat{\psi }^\dag ({\bf r})\hat{\psi }({\bf r})\rangle }_N},\) 
